Answer:
The root-mean-square (rms) velocity of gas molecules can be calculated using the formula:
\[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \]
Where:
- \( k \) is the Boltzmann constant (\(1.38 \times 10^{-23} \, \text{J/K}\)),
- \( T \) is the temperature in Kelvin,
- \( m \) is the molar mass of the gas in kilograms per mole.
For dinitrogen monoxide (N2O), the molar mass is approximately \(44.013 \, \text{g/mol}\).
Given that the temperature is \(0°C\), which is \(273.15 \, \text{K}\) in Kelvin, we can calculate:
\[ v_{\text{rms}} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \, \text{J/K} \times 273.15 \, \text{K}}{0.044013 \, \text{kg/mol}}} \]
\[ v_{\text{rms}} \approx 513 \, \text{m/s} \]
Rounded to the nearest whole number, the rms velocity is approximately \(513 \, \text{m/s}\).
